摘要:

The numerical solution of large stiff systems of ordinary differential equations is very expensive and requires large and fast computers. This is painfully clear to all who attempt to solve numerically nuclear reactor kinetics equations. The discrete form may involve as much as 100 000 ordinary differential equations and the stiffness is supplied by prompt neutrons. No wonder that reactor physicists were for years looking for some sort of simplification and this came about in the middle of the 60' as the widely used quasistatic method. Unfortunately, it had been based upon purely heuristic grounds and never left the realm of the reactor physics remaining completely unknown for the specialists in numerical solution of ordinary differential equations. In this article we show that the amplitude-shape method (ASM) which takes from the quasistatic method the representation of the solution as the product of the fast chaiiging amplitude and slow varying shape function, can be used in tlie reactor kinetics. The ASM whose full exposition is given in [5], has been developed to be applicable for numerical solution of a large class of systems of ordinary differential equations and is particularly useful in case of partial differential equations describing thc evolution of physical systems. In this paper we present the application of the ASM to the reactor kinetics equations. We present the numerical results for model equations and show that the ASM works equally well for subcritical or for supercritical systems. From [5] it follows the ASM can be also used for nonlinear problems of nuclear reactor dynamics. Practical implementation of the ASM in reactor codes is being currently investigated.

ISSN:0041-1450    

DOI:10.1080/00411459808205631

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

We study a transport problem with nonhomogeneous boundary conditions and we give the explicit form of the solution. The results are reached using the theory of affine operators, and coincide with those already known in literature found in the case of dissipative boundary conditions.

ISSN:0041-1450    

DOI:10.1080/00411459808205632

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The velocity distribution function for particles of a spatially inhomogencous gas confined in a vessel is considered as a solution of the nonlinear Boltzmann kinetic equation. Finite collision frequency is assumed. An external potential force acting upon the particles is imposed, an initial condition is given, and the interaction between the particles of the gas and the walls of the vessel is represented by a short-ranging repulsive potential force acting within a neighbourhood of the walls of the vessel. The linearization of the problem is studied, including the cases the solution cannot be approximated by a Maxwellian distribution. A sequence{fj}of iterations is constructed such thatfj+1is a solution of the problem linearized aroundfj. It is proved that the iterations converge in a convenient Banach function space to the mild solution of the original nonlinear problem provided the initial approximation is chosen close enough to the solution, and an estimate of the convergence rale is found.

ISSN:0041-1450    

DOI:10.1080/00411459808205633

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

A conference on quantum kinetic theory was held on the campus of Colorado Mountain College in the town of Breckenridge, August 4–13, 1997. The first conference in this series was held in Victoria, BC in August, 1995; a report on that meeting can be found in this journal.1The conference in Breckenridge, organized by your author and Carl Gardner of Arizona State University, perhaps might better be called a “workshop” as there were, disappointingly, only twelve participants. As a result, there were (virtually) no time limitations on the presentations; there was extensive time for discussion; and four of the participants gave second talks, for a total of 16 presentations. These papers will (hopefully) all appear in the Conference Proceedings to be published inVSLI Designwith Carl Gardner as guest editor. There was a maximum of three talks per day, allowing plenty of time for the previously-mentioned discussions as well as free time for enjoying the many attractions which Breckenridge, one of the premier vacation destinations in the western United States, has to offer.

ISSN:0041-1450    

DOI:10.1080/00411459808205634

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411459808205620

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor